SPARSENESS, CONSISTENCY AND MODEL SELECTION FOR MARKOV REGIME-SWITCHING GAUSSIAN AUTOREGRESSIVE MODELS

We study Markov regime-switching Gaussian autoregressive models that capture temporal heterogeneity exhibited by time series data. Constructing a Markov regime-switching model requires making several specifications related to the state and observation models. In particular, the complexity of these models must be specified when fitting to a data set. We propose new regularization methods based on a conditional likelihood for simultaneous autoregressive-order and parameter estimation, with the number of regimes fixed. We use a regularized Bayesian information criterion to select the number of regimes. Unlike existing information-theoretic approaches, the proposed methods avoid an exhaustive search of the model space for model selection, and thus are computationally more efficient. We establish the large-sample properties of the proposed methods for estimation, model selection, and forecasting. We also evaluate the finite-sample performance of the methods using simulations, and apply them to analyze two real data sets.